FWIW: You can buy a “Bump Fighter” razor for $8 on Amazon. That is the reusable handle style, not the disposable type. The razor handle is great and fits Gillette Trac 2 cartridges.
Of course, Gillette’s copyright is gone, so you can then buy “100 Personna Twin 2 ( TWIN II ) Razor blades - Compatible with Gillette’s Trac 2 Razor system” for under $20. I got them once for $10 & have seen them on Amazon for $15...but definitely under $20 for 100. 20 cents each or less.
I never tried the 5 bladed Gillettes, but the Trac 2 does me as well as the Mach 3 ever did.
I also like the Double Edge razors. The Merkur open comb metal one runs under $35, and DE blades run 10 cents each.
Also: When shaving with a DE razor, I just use cheap shaving cream. No special brushes. No scented soaps. Just no name shaving cream. Works fine.
If you want to use a soap, I recommend Ivory. Works fine. Cheap. Cleans your hands, too.